Work: does distance HAVE to be linear?

[camacru]

In the defining the concept of "work", does it have to a defined as a force being applied to an object over a LINEAR distance?

Take, for example, the work produced by an electric garage door closer. If you happen to have an overhead folding garage door, the motor applies the force to the drive mechanism, which in turn opens or closes the door, however, the door does simply travel vertically or horizontally; it travels along a rail which has a bend of approximately 90 deg. Is this not considered work?

 

[dx]

No, it doesn't have to be linear. You can have any kind of path.

$$W = \int F \cdot ds$$

See the PF library entry: work done

 

[Dr.D]

The integral of torque with respect to angle turned is work just as much as the integral of force with respect to distance is work.